On multidimensional consistent systems of asymmetric quad-equations

2012/01/05 by Raphael Boll, Boll, Raphael · 1 citation
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Differential Equations and Dynamical Systems #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #math-ph #math.MP #nlin.SI

paper · pdf · doi:10.48550/arxiv.1201.1203

16 pages, 17 figures

arxiv created 2012/01/05 · openalex publication_date 2012/01/05 · arxiv updated 2012/01/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Multidimensional Consistency becomes more and more important in the theory of discrete integrable systems. Recently, we gave a classification of all 3D consistent 6-tuples of equations with the tetrahedron property, where several novel asymmetric systems have been found. In the present paper we discuss higher-dimensional consistency for 3D consistent systems coming up with this classification. In addition, we will give a classification of certain 4D consistent systems of quad-equations. The results of this paper allow for a proof of the Bianchi permutability among other applications.

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